Gravitation Question 217
Question: Two wires are made of the same material and have the same volume. However, wire 1 has cross-sectional area $ [A] $ and wire 2 has cross-sectional area$ [3A] $ . If the length of wire 1 increases by Ax on applying a force $ [F] $ , how much force is needed to stretch wire 2 by the same amount?
Options:
A) $ [F] $
B)$ [4F] $
C) $ [6F] $
D) $ [9F] $
Show Answer
Answer:
Correct Answer: D
Solution:
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$ [A_{1}l_{1}=A_{2}l_{2}] $
$ [\Rightarrow l_{2}=\frac{A_{1}l_{1}}{A_{2}}=\frac{A\times l_{1}}{3A}] $
$ [\Rightarrow \frac{l_{1}}{l_{2}}=3] $ $ [\Delta x_{1}=\frac{F_{1}}{A\gamma }\times l_{1}] $
$ [\Rightarrow x_{2}=\frac{F_{2}}{3A\gamma }\times l_{1}] $ Here $ [\Delta x_{1}=\Delta x_{2}] $
$ [\frac{F_{2}}{3A\gamma }l_{2}=\frac{F_{1}}{A\gamma }l_{1}\Rightarrow F_{2}=3F_{1}\times \frac{l_{1}}{l_{2}}=3F_{1}\times 3=9F] $
